Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2001-05-31
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
30 pages, plain TeX, no figures
Scientific paper
10.1103/PhysRevB.65.035320
In this article, we shall focus on the collective dynamics of the fermions in a $\nu = 1$ quantum Hall droplet. Specifically, we propose to look at the quantum Hall ferromagnet. In this system, the electron spins are ordered in the ground state due to the exchange part of the Coulomb interaction and the Pauli exclusion principle. The low energy excitations are ferromagnetic magnons. In order to obtain an effective Lagrangian for these magnons, we shall introduce bosonic collective coordinates in the Hilbert space of many-fermion systems. These collective coordinates describe a part of the fermionic Hilbert space. Using this technique, we shall interpret the magnons as bosonic collective excitations in the Hilbert space of the many-electron Hall system. Furthermore, by considering a Hall droplet of finite extent, we shall also obtain the effective Lagrangian governing the spin collective excitations at the edge of the sample.
Ray Rashmi
Sakita Bunji
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